The Highway Safety Department wants to study the driving habits of individuals. A sample of 41 cars traveling on the highway revealed an average speed of 60 miles per hour and a standard deviation of 7 miles per hour. The population of car speeds is approximately normally distributed. Determine a 90% confidence interval estimate for the speed of all cars.

58,21    ≤   μ  ≤   61,79

Step-by-step explanation:

Normal Distribution

Poputation size        n = 41

Population mean         X  = 60

Population standard deviation    σ = 7

Question is: Confidence Interval 90 % ??

As Confidence Interval is 90 %   then  α  = 10 %

And as we are dealing with a two tail test

α/2  = 0,05

We look in Z table for values for  α/2  = 0,05  and find

z(α/2)  =  - 1,64      and    z(α/2) =  1,64

Then

Confidence Interval is

X - Zα/2 * σ/√n   ≤  μ  ≤  X + Zα/2 * σ/√n

60 - ( 1,64 ) * 7/√41  ≤   μ  ≤  60 + ( 1,64 ) * 7/√41

60 -  1,64 * 1,09375   ≤   μ  ≤  60 +  1,64 * 1,09375

60 - 1,79375    ≤   μ  ≤  60 +  1,79375

58,21    ≤   μ  ≤   61,79

x =-.20752

step-by-step explanation:

4^(x+2)=12

4^(x+2)=12

take the log base 4 on each side

log 4 (4^(x+2) = log 4(12)

we know log b(a^y) = y log b (a)

(x+2) log 4(4) = log 4 (12)

x+2 = log 4 (12)

we know   logb c = loga c/loga b

we want to convert to base 10   so a = 10

by default, we do not write the 10   c = 4   and b = 10

log4 10 = log 12/log 4

log4 10 = log 12/ log 4

x+2 = log 12/ log 4

subtract 2 from each side

x +2 -2 = log 12/ log 4 -2

x = 1.79248125 -2

x =-.20752

step-by-step explanation: